August 10th, 2016, 07:12 AM  #1 
Newbie Joined: Aug 2016 From: Ireland Posts: 2 Thanks: 0  rate of change/of a line
Hi I'm studying for a calculus test I understand how to get a slope and when a number is beside an x when written as an eqution y = mx + 1 the variable for x will be the slope but in my question the slope is x^2(x squared) which is totally confusing me,can anyone help walk me through how to get the answer here is the question If two variables x and y are related by the equation y = 3x^2 – x calculate the average rate of change of y with respect to x as x varies from 3 to 5. thanks, 
August 10th, 2016, 07:41 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,982 Thanks: 1575 
if $y = f(x) = 3x^2x$, then the average rate of change of $f(x)$ is $\dfrac{f(5)f(3)}{53}$

August 10th, 2016, 08:56 AM  #3 
Math Team Joined: Jul 2011 From: Texas Posts: 2,982 Thanks: 1575 
note that the average rate of change is the slope of the $\color{red}{line}$ connecting the two points on the curve ... $(3,f(3))$ and $(5,f(5))$

August 10th, 2016, 09:08 AM  #4 
Newbie Joined: Aug 2016 From: Ireland Posts: 2 Thanks: 0 
thanks for the reply Skeether much appreciated how come we sub in both 3 and 5 I thought they are both x values? I thought we could only sub in y and x to the slope formula? thanks, 
August 10th, 2016, 09:33 AM  #5 
Math Team Joined: Jul 2011 From: Texas Posts: 2,982 Thanks: 1575 
y is a function of x ... in other words, the value of y depends on the value of x at $x = 5$, $y = f(5) = 3(5)^2  5$ at $x = 3$, $y = f(3) = 3(3)^2  3$ slope = $\dfrac{y_2y_1}{x_2x_1} = \dfrac{f(5)f(3)}{53}$ Last edited by skeeter; August 10th, 2016 at 09:41 AM. 

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